As one of the most important elements in astronomy, iron abundance determinations need to be as accurate as possible. We investigate the accuracy of spectroscopic iron abundance analyses using archetypal metal-poor stars. We perform detailed 3D non-LTE radiative transfer calculations based on 3D hydrodynamic STAGGER model atmospheres, and employ a new model atom that includes new quantum-mechanical neutral hydrogen collisional rate coefficients. With the exception of the red giant HD122563, we find that the 3D non-LTE models achieve Fe I/Fe II excitation and ionization balance as well as not having any trends with equivalent width to within modelling uncertainties of 0.05 dex, all without having to invoke any microturbulent broadening; for HD122563 we predict that the current best parallax-based surface gravity is overestimated by 0.5 dex. Using a 3D non-LTE analysis, we infer iron abundances from the 3D model atmospheres that are roughly 0.1 dex higher than corresponding abundances from 1D MARCS model atmospheres; these differences go in the same direction as the non-LTE effects themselves. We make available grids of departure coefficients, equivalent widths and abundance corrections, calculated on 1D MARCS model atmospheres and horizontally and temporally averaged 3D STAGGER model atmospheres.